Question

In the figure intensity from each slit $S_1$, $S_2$ and $S_3$ is $I_0$ at P. Wavelength of light is $\lambda$ (D >> d)
List - 1 gives some values and List - 2 gives corresponding intensity at P. If space between slits and screen is filled with fluid of refractive index $\frac{3}{2}$ then correct match is
$\begin{array}{cccc}& \text{List-1}& & \text{List-2}\\ \text{I}& \frac{d^2}{D}=\lambda & \text{P}& I_0\\ \text{II}& \frac{d^2}{D}=\frac{\lambda }{2}& \text{Q}& 4I_0\\ \text{III}& \frac{d^2}{D}=1.5\lambda & \text{R}& 5I_0\\ \text{IV}& \frac{d^2}{D}=2\lambda & \text{S}& 9I_0\\ & & \text{T}& 3I_0\\ & & \text{U}& \text{None}\end{array}$

• A. $I\to P,II\to R,III\to S,IV\to U$
• B. $I\to R,II\to P,III\to P,IV\to P$
• C. $I\to P,II\to R,III\to T,IV\to S$
• D. $I\to P,II\to R,III\to P,IV\to S$

Answer 1

The correct option is B $I\to R,II\to P,III\to P,IV\to P$

$I\to R,II\to P,III\to U,IV\to P$

$\Delta \varphi =\frac{2\pi }{\lambda }\Delta x_{optical}$

$\Delta x_{23}=\frac{2d^2}{D}\mu ,\Delta x_{13}=\frac{9}{2}\frac{d^2}{D}\mu$

I) ${\varphi }_{23}=4\pi \times \frac{3}{2}=6\pi$ and ${\varphi }_{13}=9\pi \times \frac{3}{2}=\frac{27}{2}\pi \Rightarrow I=5I_0$

II) ${\varphi }_{23}=2\pi \times \frac{3}{2}=3\pi$ and ${\varphi }_{13}=\frac{9\pi }{2}\times \frac{3}{2}=\frac{27}{4}\pi \Rightarrow I=I_0$

III) ${\varphi }_{23}=9\pi$ and ${\varphi }_{13}=\frac{81}{4}\pi \Rightarrow I=I_0$

IV) ${\varphi }_{23}=8\pi \times \frac{3}{2}=12\pi$ and ${\varphi }_{13}=18\pi \times \frac{3}{2}=27\pi \Rightarrow I=I_0$